I've had this experience before and it is always with doctors. My doctor wants to see me every six months to evaluate my labs and renew a prescription. But one can only book an appointment 4 weeks in advance.
They justify that by saying it is "fare" that everyone get a chance to visit the doctor and booking far in advance means some people won't be seen.
The doctor sees x number of patients in any 4 week period. Some people will not be seen. It seems to me that scheduling the people the doctor wants to see would be a high priority -- especially when we are talking about renewing prescriptions.
Stacey has the same problem with her doctors.
I suspect the unspoken reason is about missed appointments. Book to far in advance and people will miss more appointments. But that is manageable. And, in fact, managing it would be good customer service. And it can be mostly automated.
The Navy hospital has an automated reminder system.
Oh well.